bunsenlabs is based on jessie.
whichever package managing software you use, graphical synaptic or command line apt-get, you should not agree 'Y' to uninstall packages that you think you might need.
3 thoughts on this whole thing:
- libavcodec is an audio/video codec. are you sure you need this to manage your notes? have you tried installing with --no-install-recommends?
- at its root this is most probably a version problem. different versions of libavcodec-whatever cannot coexist, so apt needs to remove one, resulting in an overthrowing of half your system.
- nevernote requires java-runtime, which in turn most probably pulls in all those dependencies. try installing java first.
ultimately, i hope you posted this on bunsenlabs forums, you will get much better support there.